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Tham khảo tài liệu 'computational intelligence in automotive applications by danil prokhorov_8', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | On Learning Machines for Engine Control 129 where 9 contains all the weights wkj and biases bk of the n hidden neurons together with the weights and bias fi 2 b2 of the output neuron and where the activation function g is a sigmoid function often the hyperbolic tangent g x 2 1 e -Ỵ 1 . On the other hand choosing a Gaussian function g x exp x2 ơ2 as basis function and a radial construction for the inputs leads to the radial basis function network RBFN 38 of which the output is given by n f v 9 d ag ll YkIU a0 3 k 1 _ 1 j M ak exp I 2 ------2------ I ao where Yk Yki. YkpV is the center or position of the kth Gaussian and Y ki . -kp T its scale or width most of the time with -kj -k Vj or even -kj - Vj k. The process of approximating nonlinear relationships from data with these models can be decomposed in several steps Determining the structure of the regression vector p or selecting the inputs of the network see e.g. 46 for dynamic system identification Choosing the nonlinear mapping f or in the neural network terminology selecting an internal network architecture see e.g. 42 for MLP s pruning or 37 for RBFN s center selection Estimating the parameter vector 9 i.e. weight learning or training Validating the model This approach is similar to the classical one for linear system identification 29 the selection of the model structure being nevertheless more involved. For a more detailed description of the training and validation procedures see 7 or 36 . Among the numerous nonlinear models neural or not which can be used to estimate a nonlinear relationship the advantages of the one hidden layer perceptron as well as those of the radial basis function network can be summarized as follows they are flexible and parsimonious nonlinear black box models with universal approximation capabilities 6 . 2.2 Kernel Expansion Models and Support Vector Regression In the past decade kernel methods 44 have attracted much attention in a large variety of fields and applications .
